Modern gas turbine engines, such as high bypass ratio civil aeroengines, are highly complex machines. Because of the need for realistic development times and the need to reduce costs, components and systems of a new engine have to be developed simultaneously and often without access to an actual prototype engine.
Engine performance models such as thermodynamic simulators are thus of crucial importance for engine development. Typically, they are functional models of the engine in which a plurality of linked modules or “bricks” model different components of the engine. The bricks have inputs and outputs connecting them to other bricks and each brick can be a complex model of the respective component in its own right. Such performance models are, therefore, highly non-linear and can require large numbers of iterative calculations in order to arrive at a solution for a given operating condition. Even with present day computing resources, such models are often not practically useable on the occasions when it is necessary to explore or obtain results for a range of operating conditions.
In view of the long solution times of non-linear engine performance models, it is desirable, therefore, to replace such models with faster models. One approach is to simulate the non-linear model with a piecewise linear engine performance model.
For example, Henrion, Reberga, Bernussou and Vary, Linearisation and Identification of Aircraft Turbofan Engine Models, IFAC Symposium on Automatic Control in Aerospace, Jun. 14-18, 2004, St Petersburg, Russia, discloses a piecewise linear engine performance model which simulates a highly nonlinear model of a high by-pass two-shaft gas turbine civil aircraft engine. The piecewise linear model was based on the state space representation:{dot over (x)}=Ax+Bu andy=Cx+Du, where u, x and y are vectors respectively corresponding to engine control variables u (e.g. fuel flow and inlet guide vane position), engine state variables x (e.g. rotor speeds and metal temperatures) and the engine performance variables y (e.g. gas pressures and temperatures), {dot over (x)} is a vector corresponding to the time derivatives of the engine state variables x, and A, B, C and D are matrices of partial derivatives of the variables.